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StrangelyQuarky

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## Homework Statement

A pendulum of length [itex] l [/itex] at the north pole is moving in a circle to the east at an angle [itex] \theta [/itex] to the vertical. It has some period [itex] T_E [/itex] as measured in the rotating Earth frame. The experiment is then repeated except now the pendulum is moving to the west with period [itex] T_W [/itex]. The question asks which period is longer, and to calculate the relative time difference in the periods.

## Homework Equations

In the rotating frame, the equation of motion of the pendulum involves the Coriolis force and a modified gravitational acceleration due to the rotation of the Earth: [tex] m\mathbf{a'} = m\mathbf{g'} + \mathbf{T} -2m(\mathbf{\omega '} \times \mathbf{v'}) [/tex]

where T is the tension in the wire.

## The Attempt at a Solution

Since the Earth rotates counterclockwise as viewed looking down on the north pole, the pendulum that moves to the east has a longer period because the Earth's rotation means it has to "catch up" with the rotating ground (I think?). However, I am at a loss as to how to calculate the period from equation of motion.